═══════════════════════════════════════════════════════════════ 📦 VERSION 1 (Ring Topology, IBM Hardware) — ARCHIVED ═══════════════════════════════════════════════════════════════ This OSF package constitutes Version 1 of the TCR experimental record. No additional data or analyses will be added to this registration. USPTO Provisional Patent: 63/960,327 (Filed January 14, 2026) ═══════════════════════════════════════════════════════════════ This project investigates whether optimal continuous gate parameters in quantum circuits are determined by the topological structure of the circuit’s interaction graph, rather than by empirical tuning alone. We study a family of ring-entangled quantum circuits (TICE architecture) implemented on real IBM Quantum hardware and test the hypothesis that certain cyclotomic angles (e.g., sin(π/11), sin(π/9)) produce systematically improved performance compared to a nearby empirically derived baseline parameter (λ_Q ≈ 0.341635). To rigorously control for temporal drift, hardware calibration variation, and compilation artifacts, we employ a preregistered ABBA experimental design, in which baseline (A) and candidate (B) circuits are interleaved in a balanced sequence (A→B→B→A) across multiple blocks, backends, and measurement bases. All circuits are executed with fixed qubit mappings, fixed transpiler seeds, and identical compilation constraints. Primary outcomes are evaluated using measurement distribution purity (MDP = Σ p²), with secondary analyses including alternative measurement bases (X vs Z) and paired statistical tests. All raw job IDs, measurement counts, circuit definitions, and analysis scripts are preserved to enable full reproducibility. This OSF project serves as the preregistered confirmatory record for testing an architecture-dependent cyclotomic resonance hypothesis in quantum circuit control. Exploratory results motivating this preregistration are clearly distinguished from confirmatory analyses conducted under the ABBA protocol
═══════════════════════════════════════════════════════════════ 📦 VERSION 1 (Ring Topology, IBM Hardware) — ARCHIVED ═══════════════════════════════════════════════════════════════ This OSF package constitutes Version 1 of the TCR experimental record. No additional data or analyses will be added to this registration. USPTO Provisional Patent: 63/960,327 (Filed January 14, 2026) ═══════════════════════════════════════════════════════════════ This project investigates whether optimal continuous gate parameters in quantum circuits are determined by the topological structure of the circuit’s interaction graph, rather than by empirical tuning alone. We study a family of ring-entangled quantum circuits (TICE architecture) implemented on real IBM Quantum hardware and test the hypothesis that certain cyclotomic angles (e.g., sin(π/11), sin(π/9)) produce systematically improved performance compared to a nearby empirically derived baseline parameter (λ_Q ≈ 0.341635). To rigorously control for temporal drift, hardware calibration variation, and compilation artifacts, we employ a preregistered ABBA experimental design, in which baseline (A) and candidate (B) circuits are interleaved in a balanced sequence (A→B→B→A) across multiple blocks, backends, and measurement bases. All circuits are executed with fixed qubit mappings, fixed transpiler seeds, and identical compilation constraints. Primary outcomes are evaluated using measurement distribution purity (MDP = Σ p²), with secondary analyses including alternative measurement bases (X vs Z) and paired statistical tests. All raw job IDs, measurement counts, circuit definitions, and analysis scripts are preserved to enable full reproducibility. This OSF project serves as the preregistered confirmatory record for testing an architecture-dependent cyclotomic resonance hypothesis in quantum circuit control. Exploratory results motivating this preregistration are clearly distinguished from confirmatory analyses conducted under the ABBA protocol
We report the discovery of Topological Cyclotomic Resonance (TCR), a phenomenon where quantum circuits on ring topologies exhibit optimal fidelity at a rotation parameter λ* = sin(π/11). Using IBM Quantum hardware (ibm_fez, ibm_torino) with 960,000 total shots and rigorous ABBA drift-cancellation protocols, we observe the predicted resonance with 8.4σ significance (p < 10⁻¹⁶). The constant generalizes to λ*_V = sin(π/(2V+1)) for V-qubit rings, connecting quantum computing to cyclotomic field theory. All data, code, and preregistration documents are publicly available.
This deposit contains a reproducible replication package and raw results for a multi-topology hardware validation of Topological Cyclotomic Resonance (TCR) on IBM Quantum backends ibm_fez and ibm_torino. We test the closed-form parameter ruleλ*(V) = sin(π/(2V+1))across five circuit topologies (ring, star, mesh, tree, line) and three problem sizes (V=10, 15, 20), using an ABBA interleaved design for drift control. The package includes raw and summary JSON outputs, a SHA256 manifest, analysis tables, and code/configuration needed to reproduce the experiment (tokens are not included; IBM credentials are provided via environment variables).DOI: 10.5281/zenodo.18357071 | OSF: https://osf.io/xuebt/ | ORCID: https://orcid.org/0009-0007-7286-3373
We report systematic experimental observation of coherent, topology-dependent inter-horizon correlations in thermofield double (TFD) states implemented on IBM quantum processors. Using a 100-qubit ladder geometry mapped onto the heavy-hex topology of ibm_fez (156 qubits, Heron r2 architecture), we demonstrate signal ratios R_fit spanning 1.2–202.7 across runs/seeds, with best single-seed R_fit = 23.93 (Run #11) and record multi-seed median R_fit = 102.7 (Run #2, 5 seeds, range 63.5–202.7), validated by pre-registered GO/NO-GO criteria across 14 experimental runs spanning January 24-30, 2026. Our experimental framework incorporates two rigorous anti-artifact controls (see Fig. 6-7): (1) SCRAMBLE control applies identical circuit depth with incorrect topology, destroying the signal (reduction factor > 10×); (2) ECHO control (Loschmidt reversal) applies the coupling layer twice, annihilating coherent contributions (reduction factor 8.6-50.5×, consistent with expected finite-size echo saturation for N~50 effective subsystems (see Gorin et al. [14] for saturation plateau theory)). Both controls maintain > 95% local fringe retention, confirming they do not trivially destroy coherence. A critical discovery emerged from our January 30, 2026 validation campaign (see Fig. 5): quantum processor calibration drift can cause signal collapse within less than one hour on hardware with identical offline calibration snapshots. Runs #11-#12 achieved R_fit = 23.93 and 18.4 respectively (GO-1 PASS, GO-3 PASS), while Run #13 executed only 53 minutes later on the same backend collapsed to R_fit = 1.20 (GO-1 FAIL). This finding establishes that offline Health Scores do not reliably predict experimental success, and defines an operational envelope requiring Health > 80% (Grade B or better) for empirically associated with high-probability signal stability. The observed second-harmonic (2ω) dominance in the phase-dependent signal (A₂ω/A₁ω > 40×, R² > 0.99, see Fig. 9) is consistent with theoretical predictions for bilinear left-right correlations. A stride sweep (s = 2-5, see Fig. 4) reveals a signal-coherence trade-off, with s = 3 identified as optimal. Total quantum processor time across all 14 runs: approximately 45 minutes. These results establish a validated, falsifiable experimental framework for probing analog quantum gravity signatures on NISQ hardware, with explicit calibration-conditional bounds. The methodology may provide a validated framework applicable to analog Hawking radiation platforms where topology-controlled correlations play a central role (see Section 5.4). Note: Results demonstrated primarily on IBM ibm_fez; multi-device validation on additional backends is recommended to establish cross-platform generalizability.
# Invitation to read and audit — Paper B ## What this article proposes This article presents an experimental characterization of topological quantum circuits and entangled states on heterogeneous superconducting processors: **IBM Quantum Heron** (*ibm_fez*, *ibm_marrakesh*, *ibm_kingston*) and **Origin Wukong** (*WK_C180*, *WK_C180_2*). The goal is to document, in an auditable form, the execution of GHZ states, Borromean/RSI circuits, QTDA protocols for Betti numbers and Grover algorithms on real hardware, with the proper separation of measured data, derived metrics, interpretations and hypotheses. The paper is part of a larger program — OmniMind — where the operator builds a living laboratory of physics, biology, psychoanalysis and engineering. No execution is presented as "proof of consciousness"; what is offered are real measurements, verifiable provenance and an invitation to reproducibility. ## Experiments performed ### 1. Overall scale - **723 runs** on real quantum hardware; - **5.013.322 million accumulated shots**; - **496 hardware encounters** (executions on distinct QPUs/configurations); - **IBM backends:** `ibm_fez`, `ibm_marrakesh`, `ibm_kingston`; - **Origin Wukong backends:** `WK_C180`, `WK_C180_2`; - Data kept in the canonical SQLite database `ibm_quantum_runs.db`. ### 2. GHZ states - **GHZ-4**, **GHZ-6** and **GHZ-8** executed on heterogeneous processors; - Coherence and parity measurement with **Zero Noise Extrapolation (ZNE)** and **Dynamical Decoupling (DD)**; - Evaluation of the *optimal chain* and *optimal star* GHZ-8, with IBM × Wukong comparison. ### 3. Borromean and RSI circuits - Construction and measurement of **Borromean/RSI circuits** on multiple qubits; - Estimation of topological stability parameters (C3, C4, n); - **Audited erratum:** the correct values for the Kingston set are `C3 = 0.352 ± 0.025`, `C4 = 1.213 ± 0.068`, `n = 15`; previous values (`0.514 ± 0.060`; `1.888 ± 0.131`) did not match the canonical database and were corrected. ### 4. QTDA and Betti numbers - Application of **Quantum Persistent Homology / QTDA** to estimate Betti numbers of circuits; - Heuristic **Betti↔RSI** mapping explicitly declared as a mapping hypothesis, not an ontological identity; - Discussion of limits: the same Betti numbers may correspond to distinct geometries. ### 5. Grover - Validation of **2-qubit Grover** and **3-qubit Grover**; - Comparison of success metrics, fidelity and measurement errors between platforms. ### 6. Hardware characterization - Measurement and comparison of **T1/T2** decoherence times and *readout* between IBM Heron and Origin Wukong; - Record of jitter, compiler routing and queue policies of providers; - Documentation of the IBM reproducibility gap: jobs expire after approximately 30 days, and part of the original replica (Kingston) could not be re-executed — the gap is declared, not replaced by Wukong data. ## What is in the deposit - `paper.md` — canonical Markdown article; - `paper.docx` — formatted version for revision; - `paper.pdf` — final reading version; - `MANIFEST.json` — metadata and SHA-256 hashes of files; - Canonical database and reproduction notebook available via GitHub/GitLab and Kaggle (links in the repository). ## Invitation to audit and conference We invite experimental quantum physicists, computer scientists, topological mathematicians and hardware replicators to: - re-run the GHZ, Borromean/RSI, QTDA and Grover circuits on the same backends and on different backends; - verify the jobs against the canonical IDs in the `ibm_quantum_runs.db` database; - replicate the Betti analysis and discuss the Betti↔RSI mapping; - present the data at quantum computing, AI and physics conferences; - collaborate on the next round of executions, including re-running the expired IBM jobs. ## Epistemic note Empirical data carry their source (backend, job-id, database, execution) in citation. Simulated data, when used, are labeled as such. No execution is presented as "quantum coherence in a classical CPU" or as proof of consciousness. IBM × Wukong comparisons describe architectural and compiler differences, not platform equivalence.
We investigate whether a training-free thermodynamic stability metric Φ = I × ρ - α × S, computed from IBM Quantum calibration data before circuit execution, can serve as a routing signal for allocating computation between quantum hardware and classical simulation in the tested setting. Across 23 tests on real IBM Quantum hardware, we validate a Φ-based routing framework and show in direct crossover tests that LOW-Φ quantum execution can be worse than exact classical simulation for the tested classically tractable circuits: in the primary crossover test, classical simulation achieved 0.00% error while LOW-Φ quantum execution produced 8.23% error on the same circuit. Under a strict methodology with verified physical qubit binding and decisive ground truth, HIGH-Φ versus LOW-Φ error ratios ranged from 2.90x (QPE) to 30.47x (Bernstein-Vazirani) across 7 tested algorithms. The strict seven-algorithm tests constitute the primary evidence layer, while the broader 23-test suite provides supporting boundary conditions on size, depth, and reproducibility. Circuit size and depth impose additional routing boundaries: in the tested conditions, LOW-Φ execution at 15 qubits produced 94.85% error and execution at circuit depth 103 produced 67.29% error, both transitions into regimes where classical fallback was more reliable. These results support a routing decision framework in which minimum Φ across circuit qubits determines whether to execute on quantum hardware or fall back to classical simulation, with hybrid strategies retained as a natural extension. The methods described in this paper are the subject of U.S. Provisional Patent Application No. 63/956,752 (filed January 9, 2026). No license to implement or commercialize the described methods is granted by this publication. All rights reserved.